4 papers
Linear systems in P^3 with low degrees and low multiplicities
Marcin Dumnicki
We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the ca…
Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10
Marcin Dumnicki
In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on for , 8, 9, 10, i.e. systems of curves of given degree passing thr…
Regularity and non-emptyness of linear systems in
Marcin Dumnicki
The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in…
Expected term bases for generic multivariate Hermite interpolation
Marcin Dumnicki
The main goal of the paper is to find an effective estimation for the minimal number of generic points in for which the basis for Hermite interpolation consists of th…